I'm not sure if this is done by intention but one can only load files into the CSS-Engine which have a suffix of .css. So this one:
scene.getStylesheets().add(App.class.getResource("demo.fxcss").toExternalForm());
fails and this one
scene.getStylesheets().add(App.class.getResource("demo.css").toExternalForm());
succeeds
scene.getStylesheets().add(App.class.getResource("demo.fxcss").toExternalForm());
fails and this one
scene.getStylesheets().add(App.class.getResource("demo.css").toExternalForm());
succeeds